Topological mirror symmetry for parabolic Higgs bundles

We prove the topological mirror symmetry conjecture of Hausel-Thaddeus (Hausel and Thaddeus, 2001, 2003) for the moduli space of strongly parabolic Higgs bundles of rank two and three, with full flags, for any generic weights. Although the main theorem is proved only for rank at most three, most of the results are proved for any prime rank

An overview of the literature concerning the oceanography of the eastern North Atlantic region

An overview of the main oceanographic features of the eastern North Atlantic boundary, with emphasis toward the upper layers, is presented. The principal features discussed are: water mass boundaries; forcing by wind, density and tides; topographic features and effects; fronts; upwelling and downwelling; poleward flows; coastal currents; eddies. The occurrence and spatial and seasonal variability of these features is described in five regional sections: Celtic Sea and western English Channel; Bay of Biscay; western Iberia; Gulf of Cadiz; northwest Africa. This paper is intended to provide a base of physical oceanographic knowledge in support of research in fisheries, biological and chemical oceanography, and marine biology

On Eulers Rotation Theorem

Summary: It is well known that a rigid motion of the Euclidean plane can be written as the composition of at most three reflections. It is perhaps not so widely known that a rigid motion of n-dimensional Euclidean space can be written as the composition of at most n + 1 reflections. The purpose of the present article is, firstly, to present a natural proof of this result in dimension 3 by explicitly constructing a suitable sequence of reflections, and, secondly, to show how a careful analysis of this construction provides a quick and pleasant geometric path to Eulers rotation theorem, and to the complete classification of rigid motions of space, whether orientation preserving or not. We believe that our presentation will highlight the elementary nature of the results and hope that readers, perhaps especially those more familiar with the usual linear algebra approach, will appreciate the simplicity and geometric flavor of the arguments

Narasimhan-Ramanan branes and wobbly Higgs bundles

Narasimhan-Ramanan branes, introduced by the authors in a previous paper, consist of a family of BBB-branes inside the moduli space of Higgs bundles, and a family of complex Lagrangian subvarieties. It was conjectured that these complex Lagrangian subvarieties support the BBB-branes that are mirror dual to the Narasimhan-Ramanan BBB-branes. In this paper, we show that the support of these branes intersects nontrivially the locus of wobbly Higgs bundles

Unramified covers and branes on the Hitchin system

We study the locus of the moduli space of GL(n, C)-Higgs bundles on a curve given by those Higgs bundles obtained by pushforward under a connected unramified cover. We equip these loci with a hyperholomorphic bundle so that they can be viewed as BBB-branes, and we introduce corresponding BAA-branes which can be described via Hecke modifications. We then show how these branes are naturally dual via explicit Fourier-Mukai transform (recall that GL(n, C) is Langlands self dual). It is noteworthy that these branes lie over the singular locus of the Hitchin fibration. As a particular case, our construction describes the behavior under mirror symmetry of the fixed loci for the action of tensorization by a line bundle of order n. These loci play a key role in the work of Hausel and Thaddeus on topological mirror symmetry for Higgs moduli spaces. (C) 2020 Published by Elsevier Inc

SO(p,q)-Higgs bundles and Higher Teichmuller components

Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not detected by primary invariants, or because they have special geometric significance, or both. In this paper we describe new examples of such 'exotic' components in moduli spaces of of SO(p, q)-Higgs bundles on closed Riemann surfaces or, equivalently, moduli spaces of surface group representations into the Lie group SO(p, q). Furthermore, we discuss how these exotic components are related to the notion of positive Anosov representations recently developed by Guichard and Wienhard. We also provide a complete count of the connected components of these moduli spaces (except for SO(2, q), with q >= 4)

Cyclic behaviour of stone and brick masonry under uniaxial compressive loading

An experimental research concerning the uniaxial compressive behaviour of stone and brick specimens, as well as masonry prisms, is presented. Local sandstone and clay brick materials were used in order to obtain results representative with respect to local constructions. Aiming at a comprehensive material description, a set of displacementcontrolled experiments were carried out, both under monotonic and cyclic compressive loading. The procedure adopted for testing is described and the results are discussed, namely material brittleness, intrinsic variability, energy dissipation and stiffness degradation.Dans cet article une recherche expérimentale à propos du comportement en compression uniaxial de spécimens de pierre et de la brique, aussi bien que prismes de maçonnerie, est présenté. Grès et brique de l’argile locale ont été utilisés pour obtenir des résultats représentatifs en ce qui concerne les constructions locales. Avec l’objective de obtenir une description matérielle complète, un ensemble de tests contrôlé par déplacement a été emporté, sous chargement de compression monotonic et cyclique. La procédure adoptée pour tester est décrite et les résultats sont discutés, nommément la fragilité matérielle, variabilité intrinsèque des matériaux, dissipation d’énergie et déchéance de la raideur